Bleakley's current contract is due to expire in September, but her future at the BBC has been in doubt since April, after producers decided to revamp The One Show following the departure of Bleakley's co-host Adrian Chiles to ITV.
The BBC said that the effect the negotiations were having on The One Show and its audience was the major factor in its decision to drop its much criticised offer of a £900,000 pay rise to Bleakley.
"We made a full and final offer to her several weeks ago and made it clear we would not be entering into a bidding war with other channels," the BBC said.
"Christine is still unable to make a decision and therefore we have regretfully withdrawn our offer as we have to put the interests of the One Show audience first and the current uncertainty does not allow us to do that."
Bleakley previously said that she wanted to stay at the BBC so she could work with her new One Show co-host Jason Manford, but later admitted that her desire to work with Chiles again at ITV had left her "torn".